On the Problem of Optimal Path Encoding for Software-Defined Networks

TL;DR

This paper formulates the problem of optimally encoding network paths in packet headers to reduce switch state, proves its computational hardness, and offers a practical approximation algorithm with empirical validation.

Contribution

It introduces a formal mathematical model for path encoding, proves the problem's APX-hardness, and provides a 2-approximation algorithm with empirical results.

Findings

The path encoding problem is APX-hard, making exact solutions computationally difficult.

A 2-approximation algorithm effectively encodes paths with near-optimal efficiency.

Empirical results demonstrate the algorithm's practical effectiveness in network scenarios.

Abstract

Packet networks need to maintain state in the form of forwarding tables at each switch. The cost of this state increases as networks support ever more sophisticated per-flow routing, traffic engineering, and service chaining. Per-flow or per-path state at the switches can be eliminated by encoding each packet's desired path in its header. A key component of such a method is an efficient encoding of paths through the network. We introduce a mathematical formulation of this optimal path-encoding problem. We prove that the problem is APX-hard, by showing that approximating it to within a factor less than 8/7 is NP-hard. Thus, at best we can hope for a constant-factor approximation algorithm. We then present such an algorithm, approximating the optimal path-encoding problem to within a factor 2. Finally, we provide empirical results illustrating the effectiveness of the proposed algorithm.